Test: Data Representation - 1 - SSC CGL MCQ

The binary number system is highly efficient for computers because it uses only two unique digits, 0 and 1, making it easier to represent data electronically. Computers work internally using binary numbers to process information and perform calculations. Each digit in a binary number is called a bit, and the base of the binary number system is 2.

The octal number system is based on the number 8, hence it is known as the Base 8 system. It consists of 8 unique digits, from 0 to 7. Each position in an octal number represents a successive power of 8, and it is used in computing for various applications where grouping bits into sets of three is convenient.

In the hexadecimal number system, the digit 'A' represents the value 10. Hexadecimal numbers use 16 unique digits, from 0 to 9 and A to F, where each letter represents a value greater than 9. This system is commonly used in computing to represent binary numbers in a more compact and readable form.

The number system that we primarily use in our daily lives is the Decimal Number System. This system is based on the number 10, using 10 digits from 0 to 9. It is also known as the Base 10 system or the positional number system, and it is the most familiar number system for human use in everyday calculations.

The hexadecimal number system provides a shorthand method for working with binary numbers by using 16 unique digits: 0 to 9 and A to F. This allows for a compact representation of binary data, making it easier for programmers and computer systems to work with and understand binary information efficiently.

To convert a decimal number to binary, the process involves dividing the given number by 2, noting the quotient and remainder, and then repeating the division with the quotient until the quotient is 0. The remainders obtained are arranged from Most Significant Bit (MSB) to Least Significant Bit (LSB) to form the binary number.

When converting a binary number to octal, the crucial step is to make groups of 3 bits from right to left and then convert each group to a decimal number. This grouping allows for the conversion of binary to octal efficiently.

To convert a hexadecimal number to binary, the process involves grouping the hexadecimal digits in sets of 4 bits each, starting from the right and adding leading 0s if needed. Then, each group of 4 bits is converted to its binary equivalent.

Positive powers of 2 are used for the integral part and negative powers of 2 for the fractional part in binary to decimal conversion to represent the positional value of each bit in the binary number. This positional representation is crucial for accurately converting binary numbers to their decimal equivalents.

In binary conversion, the Most Significant Bit (MSB) represents the largest binary digit in the number, while the Least Significant Bit (LSB) represents the smallest binary digit. The MSB contains the highest positional value, indicating its significance in determining the value of the binary number.

To convert a decimal number to its octal equivalent, you need to divide the given number by 8, record the quotient and remainder, and repeat the process until the quotient is 0 or less than 8. Then, write each remainder from left to right, starting from the Most Significant Digit (MSD) to the Least Significant Digit (LSD). This method allows for the conversion of decimal numbers to octal numbers efficiently.

To convert octal to decimal, you multiply each digit of the octal number with powers of 8, where these powers should be positive for the integral part and negative for the fractional part. By adding all the multiplying digits, you arrive at the decimal equivalent of the octal number. This method ensures an accurate conversion between octal and decimal number systems.

To convert a decimal number to its hexadecimal equivalent, you divide the given number by 16, recording the quotient and remainder, which can be a digit from 0 to 9 or a letter from A to F. By repeating this process until the quotient is 0 or less than 16, you can obtain the hexadecimal equivalent. This method simplifies the conversion process between decimal and hexadecimal numbers.

Converting octal to hexadecimal involves first converting each digit of the octal number to binary and then converting each binary digit to its corresponding hexadecimal number. This sequential process allows for a systematic and accurate transformation from the octal number system to the hexadecimal number system.

To convert hexadecimal to octal, the first step is to convert each digit of the hexadecimal number to binary. Subsequently, you convert each binary digit to its corresponding octal number. This systematic approach ensures an accurate and efficient conversion process between the hexadecimal and octal number systems.